A foam pump has dual, coaxial air and liquid cylinders, each having a respective air and liquid piston which move together during a dispensing operation. One or more air passageways between the air cylinder and a liquid-air mixing chamber are configured to impart rotation to an airstream passing from the air cylinder to the mixing chamber to increase turbulent mixing of the air and liquid in the mixing chamber. The liquid cylinder is axially aligned with the air cylinder to provide a low profile pump which does not require a dip tube or sleeve to communicate with the bottom of the liquid source when used in an inverted application wherein the foam pump is positioned below the source of liquid. A resilient valve member in the liquid outlet is biased to close on its own to prevent leaking in the event the air and liquid pistons do not fully return to the home position.